lecture15.2014

Goals know how to expand the potential in series of

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: xpansion in multipoles ! Goals: ! * Know how to expand the potential in series of multipoles * Know how to calculate the multipole terms Lecture 15 Monday March 3, 2014 r 2 = ⇢ ✏0 The dipole moment of a single charge in space is 1. Zero in all space (and that makes sense) 2. Undefined 3. Depends on the coordinate system 4. Q/R Quadrupole Moment Term Zh 3(~ · r0 )2 r~ i (rr0 )2 dq = (3x2 Zh 3(~ · r R R R r2 ) x02 dq + 3xy x0 y 0 dq + 3xz x0 z 0 dq ~ r 0 )2 02 (rr ) Z Z Z R R2 R 000 +3+ 3xzx0 y 00 z 0 dq + 3yz ry 0)z 0 dq 0+dq z 2 3yz2 ) yzz2 dq xy x dq + (3y 2 y 2 (3 + r i dq = R 2 02 R r ) x dq + 3xy 00 R x y dq + 3xz x0 z 0 dq R 00 R 02 R 00 2 2 +3xy x y dq + (3y r ) y dq + 3yz y z dq R 00 R 00 R 02 2 2 +3xz x z dq + 3yz y z dq + (3z r ) z dq (3x 2 Extra Slides...
View Full Document

This document was uploaded on 03/29/2014 for the course PHYS 4002.001 at Minnesota.

Ask a homework question - tutors are online